91Ó°ÊÓ

To solve a linear equation, the first step is always to isolate the variable you are solving for. In our example, the variable is \(x\). Isolation means to get \(x\) by itself on one side of the equation.
Why is this important? Isolating the variable allows us to see clearly what value it holds, making it the core of solving any equation. It involves performing operations that simplify the equation until \(x\) stands alone.
Here, we need to isolate \(x\) from: \[ 8x = 64 \]
To do this, we have to remove any coefficient or constant attached to \(x\). We do this by performing the inverse operation. For multiplication, our inverse operation is division. This leads us to the next core concept.

After deciding that we need to use division to isolate the variable, we perform the same operation on both sides of the equation. This keeps the equation balanced. Think of it like a balance scale: what you do to one side, you must do to the other to keep it balanced.
In our equation: \[ 8x = 64 \]
We divide both sides by 8 to isolate \(x\): \( \frac{8x}{8} = \frac{64}{8} \).
This simplifies to: \[ x = 8 \]
Now, we have isolated \(x\) and found its value. Always make sure that the operations you perform are valid for both sides to maintain equality.

The last but crucial step is to verify your solution. Verifying means checking to ensure the value we found for \(x\) is correct. This step helps you confirm that your math was done correctly.
To verify, substitute the value of \(x\) back into the original equation and see if it holds true.
For our example, the original equation was: \[ 8x = 64 \]
Substitute \(x = 8\): \[ 8 \times 8 = 64 \]
Simplify to: \[ 64 = 64 \]
Since both sides equal each other, the solution \( x = 8 \) is indeed correct. Verification should always be your final step to ensure accuracy.